Formalizing darwinism, naturalizing mathematics

Naturalizing the Applicability of Mathematics

In order to deal with the question of the applicability of mathematics this article distinguishes between natural mathematics, that is, innate mathematics, and artificial mathematics, that is, mathematics as a discipline. It argues that natural mathematics is applicable to the world because the systems of core knowledge of which it consists, being a result of biological evolution , fit in certa...

Formalizing Darwinism and inclusive fitness theory.

Inclusive fitness maximization is a basic building block for biological contributions to any theory of the evolution of society. There is a view in mathematical population genetics that nothing is caused to be maximized in the process of natural selection, but this is explained as arising from a misunderstanding about the meaning of fitness maximization. Current theoretical work on inclusive fi...

Formalizing objective mathematics

4 Axioms of ZFC 7 4.1 Axiom of extensionality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 4.2 Axiom of the empty set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 4.3 Axiom of unordered pairs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 4.4 Axiom of union . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 4.5 Axiom of infinity . . ...

Formalizing Mathematics via Predicative and Constructive Approaches

Formalized mathematics and mathematical knowledge management (MKM) are extremely fruitful and quickly expanding fields of research at the intersection of mathematics and computer science. The declared goal of these fields is to develop computerized systems that effectively represent all important mathematical knowledge and techniques, while conforming to the highest standards of mathematical ri...

Formalizing Mathematics using the Lean Theorem Prover